SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs

  • Authors:

  • Michael Codish;Jürgen Giesl;Peter Schneider-Kamp;René Thiemann

  • Affiliations:

  • Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel 84105;LuFG Informatik 2, RWTH Aachen University, Aachen, Germany 52074;Department of Mathematics & Computer Science, University of Southern Denmark, Odense M, Denmark 5230;Institute of Computer Science, University of Innsbruck, Innsbruck, Austria 6020

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper introduces a propositional encoding for recursive path orders (RPO), in connection with dependency pairs. Hence, we capture in a uniform setting all common instances of RPO, i.e., lexicographic path orders (LPO), multiset path orders (MPO), and lexicographic path orders with status (LPOS). This facilitates the application of SAT solvers for termination analysis of term rewrite systems (TRSs). We address four main inter-related issues and show how to encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (A) the lexicographic comparison w.r.t. a permutation of the arguments; (B) the multiset extension of a base order; (C) the combined search for a path order together with an argument filter to orient a set of inequalities; and (D) how the choice of the argument filter influences the set of inequalities that have to be oriented (so-called usable rules). We have implemented our contributions in the termination prover AProVE. Extensive experiments show that by our encoding and the application of SAT solvers one obtains speedups in orders of magnitude as well as increased termination proving power.